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A nim variation (Posted on 2021-12-09) Difficulty: 3 of 5
Nim games are two player strategy games where players take turns removing objects by some rules until none remain.

For this version, place N counters in a row numbered 1 to N.

A player's turn consists of taking either one counter or two counters from consecutive positions.

Whomever takes the last counter loses (this is called a misère game.)

If you were to play this game, for what values of N would you prefer go first and what should be your first move?

No Solution Yet Submitted by Jer    
Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
game laid out for N<10 | Comment 2 of 5 |
Here are all positions (winning, labeled "o" and losing, labeled "x") for N<10. All winning next moves are indicated by an underline and lead to a losing position for the opponent.

Note: for N= (1), 4, 9, the winner goes second, not first. 

A general rule to win remains illusive. Extrapolating to higher N may require a recursive code....

Edited on December 17, 2021, 9:57 am
  Posted by Steven Lord on 2021-12-17 09:15:42

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